Demodulation method using soft decision for quadrature amplitude modulation and apparatus thereof

ABSTRACT

In a soft decision method for demodulation of a received square QAM (Quadrature Amplitude Modulation) signal, the processing speed is improved, and the manufacturing expense is reduced, by using condition probability vector values, which are soft decision values. A condition judgment operation is employed.

TECHNICAL FIELD

The present invention relates to a soft decision demodulation techniquefor a Quadrature Amplitude Modulation (hereinafter, referred to as QAM)signal, and more particularly, to a soft decision demodulation methodcapable of enhancing the processing speed of soft decision demodulation.

BACKGROUND ART

The QAM scheme is capable of transmissions loading two or more bits ontoa given waveform symbol, whose waveform can be mathematically expressedin two real numbers and imaginary numbers that do not interfere witheach other. That is, in the complex number imaginary number α+βi, achange of the value a does not affect the value β. Due to that reason, aquadrature signal component can correspond to α, and an in-phase signalcomponent can correspond to β. Generally, the quadrature signalcomponent is referred to as the Q-channel, and the in-phase componentsignal is referred to as the I-channel.

A constellation diagram of QAM plots the amplitudes of such two waveswith respect to each other so as to make a-number of combinations. Thepositions of the combinations on a complex number plane should have anequal conditional probability. FIG. 2 is a diagram showing an example ofsuch a constellation diagram, whose size is 16 combinations. Also, eachof the points shown in FIG. 2 is referred to as a constellation point.Also, the binary number written under each constellation point representthe symbol assigned to that point, that is, a bundle of bits.

Generally, a QAM demodulator serves to convert signals incoming on an Ichannel and an Q channel, that is, a received signal given as α+βi, intothe original bit bundle according to the constellation points mentionedabove, that is, the constellation diagram. However, the received signalsmay not be positioned on places assigned previously, in most cases dueto the effect of noise interference, and accordingly the demodulator hasto restore the signals that have been converted due to noise. Since itis often desirable to guarantee the reliability of communication in thatthe demodulator takes charge of the role of noise cancellation, it ispossible to embody a more effective and reliable communication system byrendering the role to the next step of a channel decoder. However, sincethere is an information loss in a bit quantization process performed bya binary bit detector as in a hard decision by converting a demodulationsignal having a continuous value to corresponding discrete signals of 2levels in order to perform such a process, a similarity measure withrespect to the distance between a received signal and the constellationpoint is changed from a Hamming distance to a Euclidean distance withoutusing the binary, bit detector, so that an additional gain can beobtained.

As shown in FIG. 1, in order to modulate and transmit a signal encodedby a channel encoder and demodulate the signal in a channel demodulatorthrough a hard decision coding process, the demodulator has to have ascheme for generating the hard decision values corresponding to each ofthe output bits of a channel encoder from a receiving signal consistedof an in-phase signal component and a quadrature phase signal component.Such scheme generally includes two procedures, that is, a simple metricprocedure proposed by Nokia company and a dual minimum metric procedureproposed by Motorola, both procedures calculating LLR (Log LikelihoodRatio) with respect to each of the output bits and using it as an inputsoft decision value of the channel demodulator.

The simple metric procedure is an event algorithm that transforms acomplicated LLR calculation equation to a simple form of anapproximation equation, which has a degradation of performance due to anLLR distortion caused by using the approximation equation even though itmakes the LLR calculation simple. On the other hand, the dual minimummetric procedure is an event algorithm that uses the LLR calculatedusing a more precise approximation equation as an input of the channeldemodulator, which has the merit of considerably improving thedegradation of performance caused in the case of using the simple metricprocedure, but it has an expected problem that more calculations areneeded compared with the simple metric procedure and an its complicationis considerably increased upon embodying hardware.

DISCLOSURE OF THE INVENTION

Therefore, an object of the present invention is to solve the problemsinvolved in the prior art, and to provide a soft decision scheme fordemodulating a received Quadrature Amplitude Modulation (QAM) signalconsisting of an in-phase signal component and an quadrature phasesignal component, where a conditional probability vector value (a softdecision value corresponding to a bit position of a hard, decision) canbe obtained using a function including a conditional determinationcalculation from a quadrature phase component value and an in-phasecomponent value of the received signal, and so it is expected thatprocessing rate can be improved and the real manufacturing cost ofhardware can be reduced. In order to perform such a procedure, first, aknown form of a combinational constellation diagram of QAM and itscharacteristic demodulation scheme will be described as follows. Thecombinational constellation diagram of QAM may be generally divided into3 types or forms according to the arrangement of bit bundles assigned tothe constellation points. The first form is a form with a constellationas shown in FIGS. 2 to 4, the second is a form with a constellation asshown in FIGS. 5 to 7, and the third is a form that is not included inthis application.

A characteristic of the form or case shown in FIG. 2 can be summarizedas follows. In the case where the magnitude of the QAM is 2^(2n), thenumber of bits assigned to each constellation point becomes 2n, andconditional probability vector values corresponding to the first half ofthe number (that is, the first to n^(th) bits) are demodulated by one ofthe received signals α and β and the conditional probability vectorvalues corresponding to the second half of the number (that is, the(n+1)^(th) to the 2n^(th) bits) are demodulated by the remaining onereceiving signal. Also, an equation that is applied to bothdemodulations has the same procedure in the first half and second halfdemodulations. That is, when the value of received signal correspondingto the second half is substituted in the first half demodulation method,the result of the second half can be obtained. (Hereinafter, such formis referred to as ‘the first form’).

The characteristic of the form shown in FIG. 5 can be summarized asfollows. In the case where the magnitude of the QAM is 2^(2n), thenumber of the bits assigned to each of the constellation points becomes2n, and the demodulation method of the conditional probability vectorcorresponding to an odd-ordered bit is the same as the calculationmethod of the conditional probability vector corresponding to the nexteven-ordered bit. However, the received signal value used to calculatethe conditional probability vector corresponding to the odd-ordered bituses one of α and β according to a given combination constellationdiagram and the received signal value for the even-ordered bit is usedfor the remaining one. In other words, in the cases of the first andsecond conditional probability vector calculations, they use the samedemodulation method but the values of the receiving signals aredifferent. (Hereinafter, such form is referred to as ‘the second form’).

BRIEF DESCRIPTION OF THE DRAWINGS

The above objects, other features and advantages of the presentinvention will become more apparent by describing the preferredembodiment thereof with reference to the accompanying drawings, inwhich:

FIG. 1 is a block diagram for explaining a general digital communicationsystem;

FIG. 2 is a view showing a combination constellation diagram forexplaining a soft decision demodulation method in accordance with afirst embodiment of the present invention;

FIGS. 3 and 4 are views for explaining bit patterns in the combinationconstellation diagram shown in FIG. 2;

FIG. 5 is a view showing a combination constellation diagram forexplaining a soft decision demodulation method in accordance with asecond embodiment of the present invention;

FIGS. 6 and 7 are views for explaining bit patterns in the combinationconstellation diagram shown in FIG. 5;

FIG. 8 is a view showing a conditional probability vector decisionprocedure in accordance with the present invention as a functionalblock;

FIG. 9 is an output diagram with respect to each conditional probabilityvector of a first form of 1024-QAM;

FIG. 10 is an output diagram with respect to each conditionalprobability vector of a second form of 1024-QAM;

FIG. 11 is a view showing a function applied to a first probabilityvector of a third embodiment of the present invention;

FIG. 12 is a view showing a function applied to a second probabilityvector of the third embodiment of the present invention;

FIG. 13 is a view showing a function applied to a first probabilityvector of the fourth embodiment of the present invention;

FIG. 14 is a view showing a function applied to a second probabilityvector of the fourth embodiment of the present invention; and

FIG. 15 is a view showing a hardware configuration for the soft decisionof a first form of 64-QAM in accordance with the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Reference will now be made in detail to preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings.

The present invention remarkably improves the processing speed byapplying a conditional probability vector equation instead of a loglikelihood ratio method, being a soft decision demodulation method of asquare constellation QAM signals that is generally used in the industry.

The newly developed demodulation method of a square QAM signal isdivided into 2 forms (see the “Disclosure of the Invention” section,above), and first and third embodiments are used for the first form andsecond and fourth embodiments are used for the second form. Also, anoutput of the final conditional probability vector value covers an areabetween a real number “a” and another real number “−a”.

First, several basic prerequisites will be explained before enteringinto the description. The magnitude of the QAM can be characterized bythe mathematical expression 1 and accordingly the number of bitsassigned to each point of the constellation diagram can be characterizedby the mathematical expression 2.

Mathematical Expression 12^(2n) −QAM. n=2, 3, 4 . . .

Mathematical Expression 2the number of bits set in each point=2^(2n)

Accordingly, the number of the conditional probability vector values,being the final output values, also becomes 2n.

Now, a first embodiment for demodulating a square constellation QAMsignals of the present invention will be explained.

First, a soft decision method for a received signal in a system using asquare QAM signal constellation corresponding to the first form will beexplained. In the case of the first form, although it was mentioned thatone of the values of the quadrature phase component (real number part orα) or the in-phase signal component (imaginary number part or β) is usedto calculate the conditional probability vector corresponding to thefirst half bit combination when explaining the characteristic of thefirst form were explained, the first half and the second halfdemodulation using the value β and value α respectively, for theconvenience of understanding an output area according to thedemodulation is set as a value between 1 and −1 for the sake ofconvenience in the following description. Also, k is used as a parameterindicating the order of each bit.

A method for calculating a conditional probability vector correspondingto the case where the first bit ( that is, k is 1) in the first form canbe expressed as a mathematical expression 3, and FIG. 5 is avisualization of it.

Mathematical Expression 3

In the case of the first conditional probability vector (k=1), outputvalue is determined as

$\frac{1}{2^{n}}{\beta.}$However, the value of n is determined by the magnitude of QAM using themathematical expression 1.

A method for calculating the conditional probability vectorcorresponding to the second bit (k=2) in the first form can be expressedby a mathematical expression 4, and FIG. 6 is a visualization of it.

Mathematical Expression 4

In the case of the second conditional probability vector (k=2), theoutput value is unconditionally determined as

$c - {\frac{c}{2^{n - 1}}{{\beta }.}}$

Here, n is a magnitude parameter of the QAM in the mathematicalexpression 1, and c is a constant.

A method for calculating a conditional probability vector correspondingto a third bit to n^(th) bit (k=3, 4, . . . , n−1, n) in the first formcan be expressed as a mathematical expression 5. Here, as can be seenfrom FIG. 9, since the conditional probability vector corresponding tothe third or later bit indicates a determined iteration (v shape) form,it is noted that an expression be repeatedly used using such property.

Mathematical Expression 5

First, dividing the output diagram with a basic v-shaped form, theconditional probability vector corresponding to each bit is divided into(2^(k−3)+1) areas.

{circle around (2)} A basic expression according to the basic form isdetermined as

${\frac{d}{2^{n - k + 1}}{\beta }} - {d.}$

{circle around (3)} If finding a belonging area as the given β andsubstituting a value of |β|−m that is subtracted a middle value m ofeach area (for example, since the repeated area is one when k=4, thearea becomes 2^(n−2)≦|β|<3·2^(n−2) and the middle value becomesm=2^(n−1)) into the basic expression as a new β, the output value can bedetermined.

{circle around (4)} Finally, in the left and right outer areas among thedivided areas, that is, (2^(k−2)−1)2^(n−k+2)<|β|, the output value canbe determined by substituting the middle value of m=2^(n) and (|β|−m)value of a new β into the basic expression.

Here, d is a constant that is changed according to a value of k.

A method for calculating the conditional probability vectorcorresponding to the second half bits of the first form, that is, bitnumber n+1 to 2n can be obtained by substituting the β into α in themethod for obtaining the conditional probability vector of the firsthalf according to the characteristic of the first form. In other word,the condition that all of β in the mathematical expression 3 aresubstituted with α becomes a calculation expression of the firstconditional probability vector of the second half, that is, aconditional probability vector corresponding to (n+1)^(th) bit. Theconditional probability vector corresponding to the (n+2)^(th) bit ofthe second conditional probability vector of the second half can bedetermined by substituting β with α in the mathematical expression (4that is, the condition to calculate the second conditional probabilityvector of the first half), and the conditional probability vectorcorresponding to the bit number n+3 to 2n being the next case can bedetermined by transforming the mathematical expression to the abovedescription.

Next, a method for performing soft decisions of the received signal in asystem using a square QAM constellation corresponding to the second formwill be explained. For convenience of understanding, demodulation isperformed to determine the conditional probability vector correspondingto odd-ordered bits using the value of α and to determine theconditional probability vector corresponding to even-ordered bits usingthe value of β, and accordingly the output scope is determined between 1and −1 as is in the first form for convenience' sake.

In the second form, a method for calculating the conditional probabilityvector corresponding to the first bit (k=1) can be expressed as amathematical expression 6 and FIG. 6 is a visualization of it.

Mathematical Expression 6

{circle around (a)} In the case of the first bit (k=1), the output valueis determined as

${- \frac{1}{2^{2}}}{\alpha.}$

However, the value of n is determined by the mathematical expression 1according to the magnitude of the QAM.

In the second form, the conditional probability vector corresponding tothe second bit (k=2) can be obtained by substituting the α with β in themathematical expression 6 for calculating the first conditionalprobability vector according to the characteristic of the second form.

In the second form, a method for calculating the conditional probabilityvector corresponding to the third bit (k=3) can be expressed as amathematical expression 7.

Mathematical Expression 7If α·β≧0,

{circle around (a)} In the case of the third bit (k=3), the output valueis determined as

${\frac{c}{2^{n - 1}}{\alpha }} - {c.}$

If α·β<0, the calculation expression is determined as an expression inwhich all of α are substituted with β in the calculation expression inthe case of α·β≧0.

Here, n is a magnitude parameter of the QAM in the mathematicalexpression 1 and c is a constant.

As such, it can be another characteristic of the second form QAM thatthe conditional probability vector is obtained in the cases of α·β≧0 andα·β<0 separately. Such characteristic is applied when the conditionalprobability vector corresponding to the third or later bit of the secondform and includes a reciprocal substitution characteristic likesubstituting β with α.

An expression to obtain the conditional probability vector correspondingto the fourth bit (k=4) of the second form can be obtained bysubstituting α with β and β with α in the mathematical expression 7 usedto obtain the third conditional probability vector according to thesecond form.

The expression used to obtain the conditional probability vectorcorresponding to the fifth bit (k=5) of the second form can be obtainedby applying the mathematical expression 8. Here, as can be seen fromFIG. 10, since the conditional probability vector corresponding to thefifth or later bit indicates a v shape form, it is noted that anexpression be repeatedly used using such property. However, when theconditional probability vector corresponding to the fifth or later bitis calculated, the even-ordered determination value uses the expressionthat was used to calculate just before odd-ordered determination valueaccording to the property of the second form, which is applied when themagnitude of the QAM is less than 64 only. And, when the magnitude isover 256, the remaining part can be divided into two parts and thecalculation can be performed in the first half part and then in thesecond half part as is in the first form.

Mathematical Expression 8If α·β≧0,

{circle around (a)} First, on dividing the output diagram into a basicV-shaped form, the conditional probability vector corresponding to eachbit can be divided into (2^(k−5)+1) areas.

{circle around (b)} A basic expression according to a basic form isdetermined as

${\frac{d}{2^{n - k + 3}}{a}} - {d.}$

{circle around (c)} If finding a belonging area as the given α andsubstituting a value of |α|−m that is subtracted a middle value m ofeach area (for example, since the repeated area is one when k=6, thearea becomes 2^(n−2)≦|α|<3·2^(n−2) and the middle value becomesm=2^(n−1)) into the basic expression as a new α, the output value can bedetermined.

{circle around (d)} Finally, in the left and right outer area among thedivided areas, that is, (2^(k−2)−1)2^(n−k+2)<|α|, the output value canbe determined by substituting the middle value of m=2^(n) and (|α|−m)value of a new β into the basic expression.

In the case of α·β<0, the output value can be obtained by substituting αwith β in the expressions (a), (b), (c) and (d).

The calculation of the conditional probability vector corresponding tothe sixth bit of the second form can be obtained by substituting α withβ and β with α in the mathematical expression 8 used to obtain the fifthconditional probability vector by the property of the second form in thecase that the magnitude of the QAM is 64-QAM. However, in the case thatthe magnitude of the QAM is more than 256-QAM, the first half isobtained by dividing total remaining vectors into 2 and the second halfis obtained by substituting the received value (α and β) into theexpression of first half. At this time, changed value in the expressionof first half is the received value only, and the bit number value (k)is not changed but substituted with that of first half.

Consequently, in the case that the magnitude of the QAM is more than256, the calculation of the conditional probability vector correspondingto the fifth to (n+2)^(th) bit of the second half is determined by themathematical expression 8.

The calculation of the conditional probability vector corresponding tothe (n+3)th to the last, 2nth bit of the second form is determined bysubstituting the parameter α with β in the mathematical expression asmentioned above.

The soft decision demodulation of the square QAM can be performed usingthe received signal, that is, α+βi through the procedure describedabove. However, it is noted that although the method described abovearbitrarily determined an order in selecting the received signal andsubstituting it into a determination expression for convenience ofunderstanding, the method is applied more generally in real applicationsso that the character α or β expressed in the mathematical expressionscan be freely exchanged each other according to the combinationconstellation form of the QAM, and the scope of the output values may benonsymmetrical such as values between a and b, as well as values betweena and −a. This fact enlarges the generality of the present invention, sothat it increases its significance. Also, although the mathematicalexpressions described above seems to be very complicated, they aregeneralized for general applications so that it is realized that theyare very simple viewing them through applied embodiments.

FIRST EMBODIMENT

The first embodiment of the present invention is a case corresponding tothe first form. The first embodiment includes an example of 1024-QAMwhere the magnitude of QAM is 1024. The order selection of the receivedsignal is intended to apply α in the first half and β in the secondhalf.

Basically, QAM in two embodiments of the present invention can bedetermined as in the following expression. A mathematical expression 1determines the magnitude of QAM and a mathematical expression 2 showsthe number of bits set in each point of a combination constellationdiagram according to the magnitude of QAM.

Mathematical Expression 12^(2n)-QAM, n=2, 3, 4 . . .

Mathematical Expression 2the number of bits set in each point=2n

Basically, the magnitude of QAM in the first embodiment of the presentinvention is determined as the following expression, and accordingly theconditional probability vector value of the final output value becomes2n.

A case where 2^(2*5)−QAM equals to 1024−QAM according to themathematical expression 1 and the number of bits set in eachconstellation point equals to 2×5=10 bits according to the mathematicalexpression 2 will be explained using such mathematical expressions 1 and2. First, prior to entering into calculation expression applications, itis noted that if a calculation expression for 5 bits of the first halfamong 10 bits are known by the property of the first form, a calculationexpression for remaining 5 bits of the second half is also knowndirectly.

First, the first conditional probability vector expression is a case ofk=1, and has its output value determined as

$\frac{1}{2^{5}}\beta$unconditionally.

Next, the second (that is, k=2) conditional probability vector has itsoutput value of

$c - {\frac{c}{2^{4}}{{\beta }.}}$Here, c is a constant.

Next, the third (k=3) conditional probability vector calculationexpression is given as follows, where the basic expression according tothe basic form is determined as

${\frac{d}{2^{3}}{\beta }} - {d.}$

At this time, the calculation is divided into 2 areas, and the outputvalue is determined as

${\frac{d}{2^{3}}{\beta }} - d$if |β|<2⁴, and the output value is determined as

${\frac{d}{2^{3}}{{{\beta } - 32}}} - d$for the other cases.

Next, the fourth (k=4) conditional probability vector calculationexpression is given as follows, where the basic expression according tothe basic form is determined as

${\frac{d}{2^{2}}{\beta }} - d$and divided into 3 areas.

Here, the output value is determined as

${\frac{d}{2^{2}}{\beta }} - d$if |β|<2³, the output value is determined as

${\frac{d}{2^{2}}{{{\beta } - 16}}} - d$if 2³≦|β|<3·2³, and the output value is determined as

${\frac{d}{2^{2}}{{{\beta } - 32}}} - d$for the other case.

Next, the calculation expression of the fifth (k=5) conditionalprobability vector is given as follows, where a basic expressionaccording to the basic expression is determined as

${\frac{d}{2}{\beta }} - d$and is divided into 5 areas. Here, the output value is determined as

${{\frac{d}{2}{\beta }} - {d\mspace{14mu}{if}\mspace{14mu}{\beta }}} < {2^{2}.}$

And the output value is determined as

${\frac{d}{2}{{{\beta } - 8}}} - d$if 2²≦|β|<3·2², the output is determined as

${\frac{d}{2}{{{\beta } - 16}}} - d$if 3·2²≦|β|<5·2², the output value is determined as

${\frac{d}{2}{{{\beta } - 24}}} - d$if 5·2²≦|β|<7·2², and the output value is determined as

${\frac{d}{2}{{{\beta } - 32}}} - d$for the other cases.

Next, the calculation expression of 6^(th) to 10^(th) conditionalprobability vector is implemented by substituting α+β with α+β in thefirst to fifth conditional probability vectors according to the propertyof the first form.

SECOND EMBODIMENT

The second embodiment of the present invention is a case correspondingto the second form. The second embodiment includes an example of1024-QAM where the magnitude of QAM is 1024. The order selection of thereceived signal is intended to apply α first.

As in the first embodiment, the mathematical expression 1 determines themagnitude of the QAM, and the mathematical expression 2 indicates thenumber of bits set in each point of the combination constellationdiagram according to the magnitude of the QAM.

Mathematical Expression 12^(2n)-QAM, n=2, 3, 4 . . .

Mathematical Expression 2the number of bits set in each point=2n

Basically, the magnitude of QAM in the second embodiment of the presentinvention is determined as the above expression, and accordingly theconditional probability vector value of the final output value becomes2n.

A case where n equals to 5, that is, 2^(2*5)-QAM equals to 1024-QAMaccording to the mathematical expression 1 and the number of bits set ineach constellation point equals to 2×5=10 bits according to themathematical expression 2 will be explained when n is 5 using suchmathematical expressions 1 and 2.

First, the first conditional probability vector calculation is a case ofk=1, where the output value is determined as

$\frac{1}{2^{5}}a$unconditionally.

Next, the second (k=2) conditional probability vector calculationexpression is a case where the first calculation expression issubstituted, where the output value is determined as

$\frac{1}{2^{5}}{\beta.}$

Next, for the third (k=3) conditional probability vector calculationexpression, when αβ≧0, the following will be given, where the outputvalue is determined as

$c - {\frac{c}{2^{4}}{a}}$unconditionally.

However, c is a constant.

When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the third conditional probability vector explained just above (αβ≧0).

Next, for the fourth (k=4) conditional probability vector calculation,

(1) when αβ≧0, the following will be given, where the output value isdetermined as

$c - {\frac{c}{2^{4}}{\beta }}$unconditionally.

(2) When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the fourth conditional probability vector explained just above(αβ≧0).

Next, for the fifth (that is, k=5) conditional probability vectorcalculation expression, when αβ≧0, the following will be given, where abasic expression according to the basic form is determined as

${\frac{d}{2^{3}}{a}} - {d.}$

Here, the expression is divided into 2 areas, where if |α|<2⁴, theoutput value is determined as

${{\frac{d}{2^{3}}{a}} - d},$and the output value is determined as

${\frac{d}{2^{3}}{{{\alpha } - 32}}} - d$for other cases.

(2) When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the fifth conditional probability vector explained just above (αβ≧0).

Next, for the sixth conditional probability vector (that is, k=6), whenαβ≧0, a basic expression according to the basic form is determined as

${{\frac{d}{2^{2}}{a}} - d},$and here, the expression is divided into 3 areas, where if |α|<2³, theoutput value is determined as

${{\frac{d}{2^{2}}{a}} - d},$the output value is determined as

${{\frac{d}{2^{2}}{{{a} - 16}}} - d},$and the output value is determined as

${\frac{d}{2^{2}}{{{\alpha } - 32}}} - d$for other cases.

When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the sixth conditional probability vector explained just above (αβ≧0).

Next, for the calculation expression of the seventh (k=7) conditionalprobability vector, when αβ≧0, a basic expression according to the basicform is determined as

${{\frac{d}{2}{a}} - d},$and here, the expression is divided into 5 areas,

-   -   where if |α|<2², the output value is determined as

${{\frac{d}{2}{a}} - d},$

-   -   if 2²<|α|<3·2², the output value is determined as

${{\frac{d}{2}{{{a} - 8}}} - d},$

-   -   if 3·2²<|α|<5·2², the output value is determined as

${{\frac{d}{2}{{{a} - 16}}} - d},$

-   -   if 5·2²<|α|<7·2², the output value is determined as

${{\frac{d}{2}{{{\alpha } - 24}}} - d},$and the output value is determined as

${\frac{d}{2}{{{a} - 32}}} - d$for the other cases.

When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the seventh conditional probability vector explained just above(αβ≧0).

A method for obtaining the eighth to tenth conditional probabilityvectors is obtained by substituting α with β and β with α in theexpression to obtain the fifth to seventh conditional probabilityvectors.

Next, the second one of the method for demodulating square QAM signalwill be explained.

First, a soft decision method of the square QAM corresponding to thefirst form will be explained. In the case of the first form, whileanyone of the real number part and the imaginary number part among thereceived signal is used in order to calculate the conditionalprobability vector corresponding to the first half bit combination, thefirst half is demodulated using a value β and the second half isdemodulated using a value of α and it output scope is determined between1 and −1 for convenience's sake in the following description.

The method for calculating the conditional probability vectorcorresponding to the first bit in the first form can be expressed as themathematical expression 13 and FIGS. 3 and 11 are the visualization ofit.

Mathematical Expression 13If |β|≧2^(n)−1, the output is determined as sign(β).

Also, {circle around (2)} if |β|≦1, the output is determined as 0.9375*sign(β).

Also, {circle around (3)} if 1<|β|≦2^(n)−1, the output is determined as

${{{sign}(\beta)}\frac{0.0625}{2^{n} - 2}\left( {{\beta } - 1} \right)} + {0.9375*{{{sign}(\beta)}.}}$

However, the sign(β) means a sign of the value sign β.

In the first form, a method for calculating the conditional probabilityvector corresponding to the second bit can be expressed as themathematical 14 and FIGS. 4 and 12 are a visualization of it.

Mathematical Expression 14

{circle around (1)} If 2^(n)−2^(n(2−m))≦|β|≦2^(n)−2^(n(2−m))+1, theoutput is determined as (−1)^(m+1).

Also, {circle around (2)} if 2^(n−1)−1≦|β|≦2^(n−1)+1, the output isdetermined as 0.9375(2^(n−1)−|β|).

Also, {circle around (3)} if2^(n−1)−2^((n−1)(2−m))+m≦|β|≦2^(n)−2^((n−1)(2−m))+m−2, the output isdetermined as

${{- \frac{0.0625}{2^{n} - 2}}\left( {{\beta } - {2m} + 1} \right)} + {0.0375\left( {- 1} \right)^{m + 1}} + {0.0625.}$

Here, m=1 or m=2.

In the first form, a method for calculating the conditional probabilityvector corresponding to the third to (n−1)^(th) bits can be expressed asthe mathematical expression 15.

Mathematical Expression 15

{circle around (1)} if m*2^(n−k+2)−1≦|β|≦m*2^(n−k+2)+1, the output isdetermined as (−1)^(m+1).

Also, {circle around (2)} if (2l−1)*2^(n−k+1)−1<|β|≦(2l−1)*2^(n−k+1)+1,the output is determined as (−1)^(l+1)0.9375{|β|−(2l−1)*2^(n−k+1)}.

Also, {circle around (3)} if (P−1)*2^(n−k+1)+1<|β|≦P*2^(n−k+1)−1, theoutput depends on the value P, where if the P is odd number, the outputis determined as

${\frac{0.0625}{2^{n - K + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{({{({p + 1})}/2})} + 1}*{\beta }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 1}} + 1} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}} \right\rbrack}.$

However, if the value P is even number, the output is determined as

${\frac{0.0625}{2^{n - K + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\beta }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 1}} - 1} \right)}} \right\rbrack} + {\left( {- 1} \right)^{{p/2} + 1}.}$

Here, m=0, 1 . . . 2^(k−2), and l=1, 2, . . . 2^(k−2), also, P=1, 2, . .. 2^(k−1).

Here, k is bit number, which is an integer more than 3.

In the first form, a method for calculating the conditional probabilityvector corresponding to the nth bit of the last bit in the first halfcan be expressed as the mathematical expression 16. That is a specificcase of the mathematical expression 16, wherein k=n and the onlycondition expressions of {circle around (1)} and {circle around (2)} areapplied.

Mathematical Expression 16

{circle around (1)} If m*2²−1≦|β|≦m*2²+1, the output is determined as(−1)^(m+1).

Also, {circle around (2)} if (2l−1)*2¹−1<|β|<(2l−1)*2¹+1, the output isdetermined as 0.9375{|β|−(2l−1)*2¹}.

Here, m=0, 1, . . . 2^(n−2), and l=1, 2 . . . 2^(n−2).

A method for calculating the conditional probability vectorcorresponding to the second half bits of the first form, that is, bitnumber n+1 to 2n can be performed by substituting β with α in the methodfor obtaining the conditional probability vector of the first halfaccording to the property of the first form. That is, the conditionwhere all of β in the mathematical expression 13 is substituted with αbecomes the first conditional probability vector of the second half,that is, the conditional probability vector calculation expressioncorresponding to the (n+1)^(th) bit. Also, the conditional probabilityvector corresponding to the (n+2)^(th) bit, that is, the secondconditional probability vector of the second half can be determined bysubstituting β with α in the mathematical expression 14 that is thecondition where the second conditional probability vector of the firsthalf is calculated, and the conditional probability vector correspondingto the bit number n+3 to 2n, that is, the following cases, can bedetermined by transforming the mathematical expressions 15 and 16 asdescribed above.

Next, a soft decision method of the received signal of a square QAMcorresponding to the second form will be explained. Also, forconvenience of understanding, the value α is used to determine theconditional probability vector corresponding to the odd-ordered bit andthe value β is used to determine the even-ordered bit.

In the second form, the method for calculating the conditionalprobability vector corresponding the first bit can be expressed as themathematical expression 17 and FIG. 13 is a visualization of it.

Mathematical Expression 17

{circle around (a)} if |α|≧2^(n)−1, the output is determined as−sign(α).

Also, {circle around (b)} if |α|≦1, the output is determined as0.9375*sign(α).

Also, {circle around (c)} if 1<|α|≦2^(n)−1, the output is determined as

${{- {sign}}\mspace{11mu}(\alpha)\frac{0.0625}{2^{n} - 2}\left( {{\alpha } - 1} \right)} + {0.9375.}$However, sign(α) means the sign of the value α.

In the second form, a method for calculating the conditional probabilityvector corresponding to the second bit can be obtained by substitutingall of α with β in the mathematical expression 17 used to calculate thefirst conditional probability vector according to the property of thesecond form.

In the second form, the method for calculating the conditionalprobability vector corresponding to the third bit can be expressed asthe mathematical expression 18.

Mathematical Expression 18When α×β≧0,

{circle around (a)} if 2^(n)−2^(n(2−m))≦|α|≦2^(n)−2^(n(2−m))+1, theoutput is determined as (−1)^(m).

Also, {circle around (b)} if 2^(n−1)−1≦|α|≦2^(n−1)+1, the output isdetermined as 0.9375(|β|−2^(n−1)).

Also, {circle around (c)} if2^(n−1)−2^((n−1)(2−m))+m≦|α|≦2^(n)−2^((n−1)(2−m))+m−2, the output isdetermined as

${\frac{0.0625}{2^{n} - 2}\left( {{\alpha } - {2m} + 1} \right)} + {0.9735\mspace{11mu}\left( {- 1} \right)^{m}} - {0.0625.}$

If α×β<0, the calculation expression is determined as an expressionwhere all of α are substituted with β in the calculation expression ofthe case of α×β≧0.

As such, the method for obtaining the conditional probability vector ineach cases of α×β≧0 and α×β<0 can be said to be another property. Suchproperty is always applied when obtaining the conditional probabilityvector corresponding to the third or later bit of the second form, andthe mutual substitution property such as substituting β with α is alsoincluded in this property.

The expression for obtaining the conditional probability vectorcorresponding to the fourth bit of the second form is obtained bysubstituting α with β and β with α in the mathematical expression 18used to obtain the third conditional probability vector by the propertyof the second form in the case that the magnitude of the QAM is lessthan 64-QAM. However, the case where the magnitude of QAM is more than256-QAM is expressed as the mathematical expression 19.

Mathematical Expression 19

{circle around (a)} if m*2^(n−k+3)−1≦|α|≦m*2^(n−k+3)+1, the output isdetermined as (−1)^(m+)1.

Also, {circle around (b)} if (2l−1)*2^(n−k+2)−1<|α|<(2l−1)*2^(n−k+2)+1,the output is determined as (−1)^(l+1){0.9375|α|−0.9375(2l−1)*2^(n−k+2)}.

Also, {circle around (c)} if (P−1)*2^(n−k+2)+1<|α|≦P*2^(n−k+2)−1, theoutput is determined according to the value P, where if P is an oddnumber, the output is determined as

${{\frac{0.0625}{2^{n - K + 2} - 2}\left\lbrack {{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 2}} + 1} \right\rbrack}} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}},$

if P is an even number, the output is determined as

$\left. {{\frac{0.0625}{2^{n - K + 2} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 2}} - 1} \right)}} \right\rbrack} + \left( {- 1} \right)^{{p/2} + 1}} \right\rbrack.$

Here, k is a bit number, and m=0, 1, . . . 2^(k−3), l=1, 2, . . . ,2^(k−3), p=1, 2, . . . 2^(k−2).

An expression for obtaining the conditional probability vectorcorresponding to the fifth bit of the second form can be expressed asthe mathematical expression 20 in the case that the magnitude of QAM is64-QAM and can be applied the mathematical expression 19 in the casethat the magnitude of QAM is more than 256-QAM.

Mathematical Expression 20When α×β≧0,

{circle around (a)} if m*2²−1<|β|≦m*2²+1, the output is determined as(−1)^(m+1).

{circle around (b)} If (2l−1)*2²−1<|β|≦(2l−1, the output is determinedas 0.9375(−1)^(l+1){|β|−(2l−1)*2²}.

Here, m=0, 1, 2 and l=1, 2.

If α×β<0, the output is obtained by substituting β with α in theexpressions {circle around (a)} and {circle around (b)} according to theproperty of the second form.

The calculation of the conditional probability vector corresponding tothe sixth bit of the second form is obtained by substituting α with βand β with α in the mathematical expression 20 that is an expressionused to obtain the fifth conditional probability vector according to theproperty of the second form in the case that the magnitude of QAM is64-QAM. However, a case where the magnitude of QAM is more than 256-QAMis expressed as the mathematical expression 19.

A calculation of the conditional probability vector corresponding to theseventh to n bit of the second form is determined as the mathematicalexpression 19.

A calculation of the conditional probability vector corresponding to the(n+1)th bit of the second form is expressed as the mathematicalexpression 21 and this is a specific case of the mathematical expression19.

Mathematical Expression 21

{circle around (a)} if m*2²−1≦|α|≦m*2²+1, the output is determined as(−1)^(m+1).

Also, {circle around (b)} If (2l−1)*2¹−1<|α|≦(2l−1)*2¹+1, the output isdetermined as (−1)^(l+1){0.9375|α|−0.9375(2l−1)*2¹}.

Here, m=0, 1, . . . 2^(n−2) and l=1, 2 . . . 2^(n−2).

A calculation of the conditional probability vector corresponding to the(n+2)^(th) bit of the second form is obtained by substituting α with βand β with α in the mathematical expression 18.

A calculation of the conditional probability vector corresponding to the(n+3)^(th) to (2n−1)^(th) bit of the second form is obtained bysubstituting α with β in the mathematical expression 19. However, thebit number of the value k that is used at this time is 4 to n, which issequentially substituted instead of n+3 to 2n−1.

A soft decision demodulation of the square QAM can be implemented usingthe received signal, that is, the value of α+βi through such process.However, although the method described above arbitrarily decided theorder in selecting the received signal and substituting that into thedetermination expression for the convenience of understanding, it isnoted that it is applied in more general in its real application so thatthe character α or β expressed in the expression can be freely exchangedaccording to the combination constellation form of the QAM and the scopeof the output value can be asymmetrical such as a value between “a” and“b” as well as a value of “a” or “−a”. That enlarges the generality ofthe present invention and increases its significance. Also, although themathematical expressions described above seems to be very complicated,they are generalized for general applications so that it is realizedthat they are very simple viewing them through really appliedembodiments.

THIRD EMBODIMENT

The third embodiment of the present invention is a case corresponding tothe first form and is applied the property of the first form. The thirdembodiment includes an example of 1024-QAM where the magnitude of QAM is1024. The order selection of the received signal is intended to apply αin the first half and β in the second half. (referring to FIGS. 11 and12).

Basically, QAM in two embodiments of the present invention can bedetermined as following expression. A mathematical expression 1determines the magnitude of QAM and a mathematical expression 2 showsthe number of bits set in each point of a combination constellationdiagram according to the magnitude of QAM.

Mathematical Expression 12^(2n)-QAM, n=2, 3, 4 . . .

Mathematical Expression 2the number of bits set in each point =2n

Basically, the magnitude of QAM in the third embodiment of the presentinvention is determined as the following expression, and accordingly thenumber of the conditional probability vector value of the final outputvalue becomes 2n.

A case where 2^(2*5)-QAM equals to 1024-QAM according to themathematical expression 1 and the number of bits set in eachconstellation point equals to 2×5=10 bits according to the mathematicalexpression 2 will be explained when n is 5 using such mathematicalexpressions 1 and 2. First, prior to entering into calculationexpression applications, it is noted that if a calculation expressionfor 5 bits of the first half among 10 bits are known by the property ofthe first form, a calculation expression for remaining 5 bits of thesecond half is also known directly.

First, for the first conditional probability vector calculationexpression, if |β|>2⁵−1, the output is determined as sign(β).

However, {circle around (2)} if |β|≦1, the output is determined as0.9375*sign(β).

Also, {circle around (3)} if 2<|β|≦2⁵−1, the output is determined as

${sign}\mspace{11mu}{{(\beta)\left\lbrack {{\frac{0.0625}{2^{5} - 2}\left( {{\beta } - 1} \right)} + 0.9375} \right\rbrack}.}$

Next, for the second (that is, k=2, m=1, 2) conditional probabilityvector, if 0≦|β|≦1, the output is determined as 1.

Also, if 2⁵−1≦|β|≦2⁵, the output is determined as −1.

Also, if 2⁴−1≦|β|≦2⁴+1, the output is determined as 0.9375(2⁴−|β|).

Also, if 1≦|β|≦2⁴−1, the output is determined as

${{{- \frac{0.0625}{2^{4} - 2}}\left( {{\beta } - 1} \right)} + 1},$and if 2⁴+1≦|β|≦2⁵−1, the output is determined as

${{- \frac{0.0625}{2^{4} - 2}}\left( {{\beta } - 3} \right)} - {0.825.}$

Next, for the third (that is, k=3, m=0, 1, 2, l=1, 2, p=1, 2, 3, 4)conditional probability vector calculation expression,

{circle around (1)} If m*2⁴−1≦|β|≦m*2⁴+1, the output is determined as(−1)^(m+1).

At this time, when substituting m=0, 1, 2, if −1<|β|≦1, the output isdetermined as 1.

Also, if 2⁴−1<|β|≦2⁴+1, the output is determined as 1.

Also, if 2⁵−1<|β|≦2⁵+1, the input is determined as −1.

Also, {circle around (2)} if (2l−1)*2³−1<|β|≦(2l−1)*2³+1, the output isdetermined by substituting l=1, 2 into (−1)^(l+1)0.9375{|β|−(2l−1)*2³}.Here, if 2³−1<|β|≦2³+1, the output is determined as 0.9375(|β|−2³), andif 3*2³−1<|β|≦3*2³+1, the output is determined as −0.9375(|β|−3*2³).

Also, {circle around (3)} when (P−1)*2³+1<|β|≦P*2³−1 and substitutingP=1, 2, 3 and 4 according to whether P is odd number or even number, if1<|β|≦2³−1, the output is determined as

${{\frac{0.0625}{2^{3} - 2}\left( {{\beta } - 1} \right)} - 1},$

-   -   also, if 2³+1<|β|≦2⁴−1, the output is determined as

${{\frac{0.0625}{2^{3} - 2}\left( {{\beta } - 2^{4} + 1} \right)} + 1},$

-   -   also, if 2⁴+1<|β|≦3*2³−1, the output is determined as

${{\frac{0.0625}{2^{3} - 2}\left( {2^{4} + 1 - {\beta }} \right)} + 1},$

-   -   also, 3*2³+1<|β|≦2⁵−1, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left( {2^{5} + 1 - {\beta }} \right)} - 1.$

Next, for the fourth (that is, k=4, m=0, 1, 2, 3 and 4, l=1, 2, 3 and 4,p=1, 2, 3, 4, 5, 6, 7 and 8) conditional probability vector calculationexpression,

-   -   if −1<|⊕|≦1, the output is determined as −1.

Also, if 2³−1<|⊕|≦2³+1, the output is determined as 1.

Also, if 2⁴−1<|β|≦2⁴+1, the output is determined as −1.

Also, if 3*2³−1<|β|≦3*2³+1, the output is determined as 1.

Also, if 2⁵−1<|β|≦2⁵+1, the output is determined as −1.

Also, if 2²−1<|β|≦2²+1, the output is determined as 0.9375{|β|−2²}.

Also, if 3*2²−1<|β|≦3*2²+1, the output is determined as−0.9375{|β|−3*2²}.

Also, if 5*2²−1<|β|≦5*2²+1, the output is determined as0.9375{|β|−5*2²}. Also, if 7*2²−1<|β|≦7*2²+1, the output is determinedas −0.9375{|β|−7*2²}. Also, if 1<|β|≦2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left( {{\beta } - 1} \right)} - 1.$

Also, if 2²+1<|β|≦2³−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left( {{\beta } - 2^{3} + 1} \right)} + 1.$

Also, if 2³+1<|β|≦3*2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left( {2^{3} + 1 - {\beta }} \right)} + 1.$

Also, if 6*2²+1<|β|≦7*2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left( {{6*2^{2}} + 1 - {\beta }} \right)} + 1.$

Also, if 7*2²+1<|β|≦2⁵−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left( {2^{5} - 1 - {\beta }} \right)} - 1.$

Next, for the fifth (that is, k=5, m=0, 1, 2, . . . 7, 8, l=1, 2, 3, . .. 7, 8) conditional probability vector calculation expression,

-   -   if −1<|β|≦1, the output is determined as −1.

Also, if 2²−1<|β|≦2²+1, the output is determined as 1.

Also, if 3*2²−1<|β|≦3*2²+1, the output is determined as −1.

Also, if 7*2²−1<|β|≦7*2²+1, the output is determined as 1.

Also, if 2⁵−1<|β|≦2⁵+1, the output is determined as −1.

Also, if 1<|β|≦3, the output is determined as 0.9375(|β|−2).

Also, if 5<|β|≦7, the output is determined as −0.9375(|β|−6).

Also, if 9<|β|≦11, the output is determined as 0.9375(|β|−10).

Also, if 25<|β|≦27, the output is determined as 0.9375(|β|−26).

Also, if 29<|β|≦31, the output is determined as −0.9375(|β|−30).

Next, the calculation expressions of the sixth to tenth conditionalprobability vectors can be obtained by substituting β with α in thefirst to fifth conditional probability vector according to the propertyof the first form.

FOURTH EMBODIMENT

The fourth embodiment of the present invention is a case correspondingto the second form and is applied the property of the second form. Thefourth embodiment includes an example of 1024-QAM where the magnitude ofQAM is 1024. The order selection of the received signal is intended toapply α at first.

A mathematical expression 1 determines the magnitude of QAM and amathematical expression 2 shows the number of bits set in each point ofa combination constellation diagram according to the magnitude of QAM,as is in the third embodiment.

Mathematical Expression 12^(2n)-QAM, n=2, 3, 4 . . .

Mathematical Expression 2the number of bits set in each point=2n

Basically, the magnitude of QAM in the fourth embodiment of the presentinvention is determined as the above expression, and accordingly thenumber of the conditional probability vector value of the final outputvalue becomes 2n.

A case where 2^(2*5)-QAM equals to 1024-QAM according to themathematical expression 1 and the number of bits set in eachconstellation point equals to 2×5=10 bits according to the mathematicalexpression 2 will be explained when n is 5 using such mathematicalexpressions 1 and 2. (referring to FIGS. 13 and 14).

First, the calculation of the first conditional probability vector,

-   -   if |α|>2⁵−1, the output is determined as −sign(α).

Also, if |α|≦1, the output is determined as −0.9375 sign(α).

Also, if 1<|α|≦2⁵−1, the output is determined as

$- {{{{sign}(\alpha)}\left\lbrack {{\frac{0.0625}{2^{5} - 2}\left( {{\alpha } - 1} \right)} + 0.9375} \right\rbrack}.}$

Next, the second conditional probability vector calculation expressionis a substitution form of the first calculation expression as follows.

{circle around (a)} If |β|>2⁵−1, the output is determined as −sign(β).

{circle around (b)} if |β|≦1, the output is determined as −0.9375sign(β).

{circle around (c)} 1<|β|≦2⁵−1, the output is determined as−sign(β){0.0021(|β|−1)+0.9375.

Next, for the third conditional probability vector calculationexpression, when αβ≧0,

{circle around (a)} if 2⁵−2^(5(2−m))≦|α|<2⁵−2^(5(2−m))+1, the output isdetermined as (−1)^(m).

At this time, since m equals to 1 and 2, when substituting that, if0≦|α|<1, the output is determined as −1.

Also, if 2⁵−1≦|α|<2⁵, the output is determined as 1.

Also, {circle around (b)} if 2⁴−1≦|α|<2⁴+1, the output is determined as0.9375(|α|−2⁴).

Also, {circle around (c)} if 2⁴−2^(4(2−m))+m≦|α|<2⁵−2^(4(2−m))+m−2, theoutput is determined as

${\frac{0.0625}{2^{4} - 2}\left( {{\alpha } - {2m} + 1} \right)} + {0.9735\left( {- 1} \right)^{m}} - {0.0625.}$

Here, when substituting m=1, 2,

-   -   if 1≦|α|<2⁴−1, the output is determined as

${\frac{0.0625}{2^{4} - 2}\left( {{\alpha } - 1} \right)} - 1.$

Also, if 2⁴+1≦|α|<2⁵−1, the output is determined as

${\frac{0.0625}{2^{4} - 2}\left( {{\alpha } - 3} \right)} + {0.825.}$

When αβ<0,

in this case, the calculation expression is obtained by substituting αwith β in the expressions {circle around (a)}, {circle around (b)},{circle around (c)} of the method for determining the output of thethird conditional probability vector described just above.

Next, for the fourth (that is, k=4, m=0, 1, 2, l=1, 2, p=1, 2, 3, 4)conditional probability vector calculation,

When αβ≧0,

{circle around (a)} if m*2⁴−1≦|α|<m*2⁴+1, the output is determined as(−1)^(m+1).

At this time, substituting m=0, 1, 2, if −1<|α|≦1, the output isdetermined as −1.

Also, if 2⁴−1≦|α|<2⁴+1, the output is determined as 1.

Also, if 2⁵−1≦|α|<2⁵+1, the output is determined as −1.

Also, {circle around (b)} if (2l−1)*2³−1≦|α|<(2l−1)*2³+1, the output isdetermined by substituting l=1, 2 in the(−1)^(l+1){0.9375|α|−0.9375(2l−1)*2³},

-   -   here, if 2³−1≦|α|<2³+1, the output is determined as        0.9375(|α|−2³).

Also, if 3*2³−1≦|α|≦(3*2³+1, the output is determined as−0.9375(|α|−3*2³).

Also, {circle around (c)} if (P−1)*2³+1≦|α|≦P*2³−1 and P is an oddnumber, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left( {P - 1} \right)*2^{3}} + 1} \right\rbrack} + {\left( {- 1} \right)^{{({p + 1})}/2}.}$

However, if P is an even number, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{3}} - 1} \right)}} \right\rbrack} + {\left( {- 1} \right)^{{p/2} + 1}.}$

Here, when substituting p=1, 2, 3, 4,

-   -   if 1<|α|≦2³−1, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\alpha } - 1} \right\rbrack} - 1.$

Also, if 2³+1<|α|≦2⁴−1, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\alpha } - 2^{4} + 1} \right\rbrack} + 1.$

Also, if 2⁴+1<|α|≦3*2³−1, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left\lbrack {2^{4} + 1 - {\alpha }} \right\rbrack} + 1.$

Also, if 3*2³+1<|α|≦2⁵−1, the output is determined as

${\frac{0.0625}{2^{3} - 2}\left\lbrack {2^{5} + 1 - {\alpha }} \right\rbrack} - 1.$

When αβ<0,

in this case, the calculation expression is obtained by substituting αwith β in the expressions of {circle around (a)}, {circle around (b)},{circle around (c)} of the method for determining the output of thefourth conditional probability vector described just above.

Next, for the fifth (that is, k=5, m=0, 1, 2, 3, 4, l=1, 2, 3, 4)conditional probability vector,

-   -   (1) when αβ≦0,    -   {circle around (a)} if m*2³−1<|α|≦m*2³+1, the output is        determined as (−1)^(m+1).

At this time, when substituting m=0, 1, 2, 3, 4,

-   -   if −1<|α|≦1, the output is determined as −1.

Also, if 2³−1<|α|≦2³+1, the output is determined as 1.

Also, if 2⁴−1<|α|≦2⁴+1, the output is determined as −1.

Also, if 3*2³−1<|α|≦3*2³+1, the output is determined as 1.

Also, if 2⁵−1<|α|≦2⁵+1, the output is determined as −1.

Also, {circle around (b)} if (2l−1)*2²−1<|α|≦(2l−1)*2²+1, the output isdetermined by substituting l=1, 2, 3, 4 in the(−1)^(l+1)0.9375{|α|−0.9375(2l−1)*2³},

-   -   here, if 2²−<|α|≦2²+1, the output is determined as        0.9375(|α|=2²).

Also, if 3*2³−1<|α|≦3*2³+1, the output is determined as−09375(|α|−3*2²).

Also, if 5*2²−1<|α|≦5*2²+1, the output is determined as0.9375(|α|−5*2²).

Also, if 7*2²−1<|α|≦7*2²+1, the output is determined as−0.9375(|α|−7*2²).

Also, {circle around (c)} when (P−1)*2²+1<|α|≦P*2²−1, and substitutingp=1, 2, 3, . . . 7, 8 according to whether P is an odd number or an evennumber,

-   -   if 1<|α|≦2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - 1} \right\rbrack} - 1.$

Also, if 2²+1<|α|≦2³−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - 2^{3} + 1} \right\rbrack} + 1.$

Also, if 2³+1<|α|≦3*2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {2^{3} + 1 - {\alpha }} \right\rbrack} + 1.$

Also, if 3*2²+1<|α|≦2⁴−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {2^{4} - 1 - {\alpha }} \right\rbrack} - 1.$

Also, if 2⁴+1<|α|≦5*2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - 2^{4} - 1} \right\rbrack} - 1.$

Also, if 5*2²+1<|α|≦6*2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - {6*2^{2}} + 1} \right\rbrack} + 1.$

Also, if 6*2²+1<|α|≦7*2²−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {{6*2^{2}} + 1 - {\alpha }} \right\rbrack} + 1.$

Also, if 7*2²+1<|α|≦2⁵−1, the output is determined as

${\frac{0.0625}{2^{2} - 2}\left\lbrack {2^{5} - 1 - {\alpha }} \right\rbrack} - 1.$

When αβ<0,

in this case, the calculation expression is obtained by substituting αwith β in the {circle around (a)}, {circle around (b)}, {circle around(c)} expressions of the method for determining the fifth conditionalprobability vector (αβ<0) described just above.

Next, for the sixth conditional probability vector (that is, k=6, m=0,1, 2, . . . 7, 8, l=1, 2, 3, . . . 7, 8),

-   -   (1) when αβ≧0,

{circle around (a)} if m*2²−1<|α|≦m*2²+1, the output is determined as(−1)^(m+1).

At this time, the output is obtained by applying m=0, 1, 2, . . . 7, 8.

That is, if −1<|α|≦1, the output is determined as −1.

Also, if 2²−1<|α|≦2²+1, the output is determined as 1.

Also, if 3*2²−1<|α|≦3*2²+1, the output is determined as −1.

Also, if 7*2²−1<|α|≦7*2²+1, the output is determined as 1.

Also, if 2⁵−1<|α|≦2⁵+1, the output is determined as −1.

Also, {circle around (b)} if (2l−1)*2−1<|α|≦(2l−1)*2+1,

-   -   the output is determined by substituting l=1, 2, 3, . . . 7, 8        in the    -   (−1)^(l+1){0.9375|α|−0.9375(2l−1)*2},    -   here, if 1<|α|≦3, the output is determined as 0.9375(|α|−2).

Also, if 5<|α|≦7, the output is determined as −0.9375(|α|−6).

Also, if 9<|α|≦11, the output is determined as 0.9375(|α|−10).

Also, if 25<|α|≦27, the output is determined as 0.9375(|α|−26).

Also, if 29<|α|≦31, the output is determined as −0.9375(|α|−30).

(2) When αβ<0,

-   -   in this case, the calculation expression is obtained by        substituting α with β in the

{circle around (a)}, {circle around (b)} expressions of the method fordetermining the output of the fifth conditional probability vector(αβ≧0) described just above.

Next, the calculation expressions of the seventh to tenth conditionalprobability vector are obtained by substituting α with β and β with α inthe calculation expressions of the third to sixth conditionalprobability vector.

FIG. 14 is a view showing a functional block for a conditionalprobability vector decision process in accordance with the presentinvention.

FIG. 15 is a view showing an example of hard ware configuration for aconditional probability vector of a first form of 64-QAM in accordancewith the present invention. A person skilled in the art can configurethe hard ware by making a modification within the scope of the presentinvention.

While the present invention has been described in conjunction withpreferred embodiments thereof, it is not limited by the foregoingdescription, but embraces alterations, modifications and variations inaccordance with the spirit and scope of the appended claims.

INDUSTRIAL APPLICABILITY

In accordance with the present invention, it is expected to enhance theprocess speed remarkably and to save a manufacturing cost upon embodyinghard ware by applying a linear conditional probability vector equationinstead of a log likelihood ratio method being soft decisiondemodulation method of a square QAM signal that is generally used in theindustrial field.

1. A soft decision method for demodulating a received signal α+βi of asquare Quadrature Amplitude Modulation (QAM) consisting of an in-phasesignal component and a quadrature phase signal component, comprising:receiving the signal α+βi in a radio communication apparatus; obtaininga plurality of conditional probability vector values, each being a softdecision value corresponding to a bit position of a hard decision, usinga function including a conditional determination operation from thequadrature phase component and the in-phase component of the receivedsignal, wherein a conditional probability vector decision method fordemodulating a first half of a total number of bits is the same as adecision method for demodulating the remaining half of the bits, and isdetermined by substituting a quadrature phase component value and anin-phase component value with each other, and wherein the demodulationmethod of the conditional probability vector corresponding to anodd-ordered bit is the same as a calculation method of the conditionalprobability vector corresponding to the next even-ordered bit, where thereceived signal value used to calculate the conditional probabilityvector corresponding to the odd-ordered bit uses one of the α and βaccording to a given combination constellation diagram and the receivedsignal value for the even-ordered bit uses the remaining one of α and β.2. The method according to claim 1, wherein a first conditionalprobability vector is determined by selecting any one of the receivedsignal components α and β according to a form of a combinationconstellation diagram and then according to the following mathematicalexpression: an output value is unconditionally determined as${{- \frac{a}{2^{n}}}\Omega},$ where Ω is a selected and received valuethat is one of α and β, n is a magnitude of the QAM, that is, aparameter used to determine 2^(2n), and a is an arbitrary real numberset according to a desired output scope.
 3. The method according toclaim 2, wherein a second conditional probability vector is determinedby substituting the received value selected with the received value thatis not selected in the method for obtaining the first conditionalprobability vector.
 4. The method according to claim 1, wherein a thirdconditional probability vector is determined by selecting one of thereceived values α and β according to a form of a combinationconstellation diagram, using the following mathematical expression (B)in the case of αβ≧0, and substituting a received value selected in th emathematical expression (B) with a received value that is not selectedin the expression in the case of αβ<0, where in the mathematicalexpression (B) an output value is determined as${a\left( {c - {\frac{c}{2^{n - 1}}{\Omega }}} \right)},$ where Ω is aselected and received value, n is a magnitude of the QAM, that is, aparameter used to determine 2^(2n), a is an arbitrary real number setaccording to a desired output scope, and c is an arbitrary constant. 5.The method according to claim 4, wherein a fourth conditionalprobability vector is calculated by substituting each of the receivedvalues used with each of the received values that are not used in themethod for obtaining the third conditional probability vector in thecases of αβ≧0 and αβ<0.
 6. The method according to claim 1, wherein afifth conditional probability vector is determined by selecting one ofthe received values α and β according to the form of the combinationconstellation diagram, using the following mathematical expression (C)in the case of αβ≧0, and determines by substituting the received valueselected in the mathematical expression (C) with the received value thatis not selected in the expression in the case of αβ<0, where in themathematical expression (C), {circle around (1)} first, dividing anoutput diagram in a shape of a basic V form, and the conditionalprobability vector corresponding to each bit is divided into 2 areas,{circle around (2)} a basic expression according to a basic form isdetermined as${a\left( {{\frac{d}{2^{{\cdot n} - 2}}{\Omega }} - d} \right)},${circle around (3)} an output is determined by finding an involved areausing a given Ω and substituting a value of (|Ω|−m) that a middle valueis subtracted from each area into the basic expression as a new Ω,{circle around (4)} rendering the middle value as m=2^(n) andsubstituting the value of |Ω|−m into the basic expression as a new Ω inan area that is in the most outer left and right sides among the dividedareas, that is, 7·2^(n−3)<|Ω|, where Ω is a selected and received value,n is a magnitude of the QAM, that is, a parameter used to determine2^(2n), d is a constant, and a is a constant determining the outputscope.
 7. The method according to claim 6, wherein when the magnitude ofQAM is 64-QAM, a sixth conditional probability vector is calculated bysubstituting each of received values used with each of the receivedvalues that are not used in the method for obtaining the fifthconditional probability vector in the cases of αβ≧0 and αβ<0.
 8. Themethod according to claim 1, wherein when the magnitude of QAM is morethan 256-QAM, fifth to (n=2)^(th) conditional probability vectors aredetermined by selecting one of the received values α and β according tothe form of the combination constellation diagram, using the followingmathematical expression (D) in the case of αβ≧0, and substituting thereceived value selected in the mathematical expression (D) with thereceived value that is not selected in the case of αβ<0, where in themathematical expression (D), {circle around (1)} first, dividing anoutput diagram in a shape of a basic V form, and the conditionalprobability vector corresponding to each bit is divided into (2^(k−5)+1)areas, {circle around (2)} a basic expression according to the basicform is determined as${a\left( {{\frac{d}{2^{n - k + 3}}{\Omega }} - d} \right)},$ {circlearound (3)} an output is determined by finding an involved area using agiven Ω and substituting a value of |Ω|−m that a middle value m (forexample, in the case of k=6, since repeated area is 1, this area is2⁻²≧|Ω|<3·2^(n−2) and the middle value is m=2^(n−1)) is subtracted fromeach area into the basic expression as a new Ω, {circle around (4)}rendering the middle value as m=2^(n) and substituting the value of|Ω|−m into the basic expression as a new Ω in an area that is in themost outer left and right sides among the divided areas, that is,(2^(k−2)−1)2^(n−k+2)<|Ω|, where k is the conditional probability vectornumber (5, 6, . . . n), Ω is a selected and received value, n is amagnitude of the QAM, that is, a parameter used to determine 2^(2n), ais a constant determining the output scope, and d is a constant thatchanges according to a value of k.
 9. The method according to claim 8,wherein when the magnitude of QAM is more than 256-QAM, the (n+3)^(th)to (2n)^(th) conditional probability vectors are selected by themathematical expression (D) using the received value that is notselected when determining the fifth to (n+2)^(th) conditionalprobability vector in the case of αβ≧0, and is obtained by substitutingthe received value selected in the mathematical expression (D) with thereceived value that is not selected in the expression in the case ofαβ<0.
 10. The method according to claim 1, wherein a first conditionalprobability vector is determined by selecting any one of the receivedvalues α and β according to a form of the combination constellationdiagram and then according to the following mathematical expression (E),where in the mathematical expression (E), {circle around (1)} if|Ω|≧2^(n)−1, an output is determined as a*sign(Ω), also, {circle around(2)} if |Ω|≦1, the output is determined as a*0.9375*sign(Ω), also,{circle around (3)} if 1<|Ω|≦2^(n)−1, the output is determined as${a*{{{sign}(\Omega)}\left\lbrack {{\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - 1} \right)} + 0.9375} \right\rbrack}},$where Ω is any one of the received values α and β, ‘sign(Ω)’ indicatesthe sign of the selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value ofI (real number) channel, and β is a received value of Q (imaginarynumber) channel.
 11. The method according to claim 1, wherein a secondconditional probability vector is determined by a received valueselected when determining a first conditional probability vector and thefollowing mathematical expression (F), wherein the mathematicalexpression (F) {circle around (1)} if2^(n)−2^(n(2−m))≦|Ω|≦2^(n)−2^(n(2−m))+1, an output is determined asa*(−1)^(m+1), {circle around (2)} if 2^(n−1)−1≦|Ω|≦2^(n−1)+1, the outputis determined as a*0.9375(2^(n−1)−|Ω|), {circle around (3)} if2^(n−1)−2^((n−1)(2−m)) +m≦|Ω|≦2 ^(n)−2^((n−1)(2−m)) +m−2, the output isdetermined as${{- a}*\left\lbrack {{\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - {2m} + 1} \right)} + {0.9735\left( {- 1} \right)^{m + 1}} + 0.0625} \right\rbrack},$where Ω is a selected and received value, n is the magnitude of QAM,that is, a parameter used to determine 2^(2n), ‘a’ is an arbitrary realnumber set according to a desired output scope, and m=1,
 2. 12. Themethod according to claim 11, wherein third to (n−1)^(th) conditionalprobability vectors of the first form are determined by the receivedvalue selected when determining the first conditional probability vectorand the mathematical expression (G), where in the mathematicalexpression (G), {circle around (1)} if m*2^(n−k+2)−1<|Ω|≦m*2^(n−k+2)+1,the out is determined as a*(−1)^(m+1), also, {circle around (2)} if(2l−1)*2^(n−k+1)−1<|Ω|≦(2l−1)*2^(n−k+1)+1, the output is determined asa*(−1)^(l+1)0.9375{(|Ω|−(2l−1)*2^(n−k+1)), also, {circle around (3)} if(P−1)*2^(n−k+1)+1<|Ω|≦P*2^((n−k+1)−1, when P is an odd number, theoutput is determined as${a*\left\lbrack {\frac{0.0625}{2^{n - k + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 1}} + 1} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}} \right\rbrack} \right\rbrack},$when P is an even number, the output is determined as${a*\left\lbrack {{\frac{0.0625}{2^{n - K + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 1}} - 1} \right)}} \right\rbrack} + \left( {- 1} \right)^{{p/2} + 1}} \right\rbrack},$where m in mathematical expression (G) is 0, 1, . . . 2^(k−2), and l is1, 2, . . . 3^(k−2), k is conditional probability vector number (k=3, .. . n−1).
 13. The method according to claim 12, wherein the n^(th)conditional probability vector is determined by the received valueselected when determining the first conditional probability vector andthe following mathematical expression (H), where in the mathematicalexpression (H), {circle around (1)} if m*2²−1≦|Ω|≦m*2^(n2)+1, the outputis determined as a*(−1)^(m+1), also, {circle around (2)} if(2l−1)*2¹−1<|Ω|≦(2l−1)*2¹+1, the output is determined asa*(−1)^(l+1)0.9375{(|Ω|−(2l−1)*2¹), where m in mathematical expression(H) is 0, 1, . . . 2^(n−2) and l is 1, 2, . . . 3^(n−2).
 14. The methodaccording to claim 13, wherein the (n+1)^(th) to 2n^(th) conditionalprobability vectors are sequentially obtained using the received valuethat is not selected when determining the first conditional probabilityvector and the mathematical expressions (F) to (H), respectively, exceptthat the conditional probability vector number k included in themathematical expression (G) is sequentially used as 3 to n−1 instead ofn+3 to 2n−1.
 15. The method according to claim 1, wherein a firstconditional probability vector is determined by selecting any one of thereceived values α and β according to a form of the combinationconstellation diagram and then according to the mathematical expression(I), where in the mathematical expression (I), {circle around (1)} if|Ω|≧2^(n)−1, the output is determined as −a*sign(Ω), also, {circlearound (2)} if |Ω|≦1, the output is determined as a*0.9375*sign(Ω),also, {circle around (3)} if 1<|Ω|≦2^(n)−1, the output is determined as${{- a}*\left\lbrack {{{{sign}(\Omega)}\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - 1} \right)} + {0/9275}} \right\rbrack},$where ‘sign(Ω)’ indicates the sign of the selected and received value.16. The method according to claim 1, wherein a second conditionalprobability vector is calculated by substituting a received valueselected in a method for obtaining a first conditional probabilityvector with a received value that is not selected in the method.
 17. Themethod according to claim 1, wherein a third conditional probabilityvector is determined by selecting any one of the received values α and βaccording to a combination constellation diagram, using the followingmathematical expression (J) in the case of α*β≧0, and substituting theselected and received value in the mathematical expression (J) with thereceived value that is not selected in the mathematical expression (J)in the case of α*β<0, where in the mathematical expression (J), {circlearound (1)} if 2^(n)−2^(n(2−m))≦|Ω|≦2^(n)−2^(n(2−m))+1, the output isdetermined as a*(−1)^(m), also, {circle around (2)} if2^(n−1)−1≦|Ω|≦2^(n−1)+1, the output is determined asa*0.9375(|Ω|−2^(n−1)), also, {circle around (3)} if2^(n−1)−2^((n−1)(2−m))+m≦|Ω|≦2^(n)−2^((n−1)(2−m))+m−2, the output isdetermined as${a*\left\lbrack {{\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - {2m} + 1} \right)} + {0.9735\left( {- 1} \right)^{m}} - 0.0625} \right\rbrack},$where Ω is a selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value of1 (real number) channel, β is a received value of Q (imaginary number),and m=1,
 2. 18. The method according to claim 1, wherein when themagnitude of QAM is less than 64-QAM, a fourth conditional probabilityvector is calculated by substituting each of received values used witheach of the received values that are not used in the method forobtaining a third conditional probability vector in the cases of α*β≧0and α*β<0.
 19. The method according to claim 1, wherein when themagnitude of QAM is 64-QAM, a fifth conditional probability vector isdetermined by selecting one of the received values α and β according tothe form of a combination constellation diagram, and using the followingmathematical expression (K) in the case of α*β≧0, and substituting thereceived value selected in the mathematical expression (K) with thereceived value that is not selected in the expression in the case ofα*β<0, where in the mathematical expression (K), {circle around (1)} ifm*2^(n−1)−1≦|Ω|≦m*2^(n−1)+1, the output is determined as a*(−1)^(m+1),also, {circle around (2)} if (2l−1)*2^(n−1)−1<|Ω|≦(2l−1)*2^(n−1)+1, theoutput is determined as a*(−1)^(l+1){0.9375|β|−0.9375(2l−1)*2^(n−1)},where Ω is a selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value ofI (real number) channel, β is a received value of Q (imaginary number)channel, m=0, 1, 2, and l=1,
 2. 20. The method according to claim 1,wherein when the magnitude of QAM is 64-QAM, a sixth conditionalprobability vector is calculated by substituting each of received valuesused with each of the received values that are not used in a method forobtaining a fifth conditional probability vector of the second form inthe cases of α*β≧0 and α*β<0.
 21. The method according to claim 1,wherein when the magnitude of QAM is more than 256-QAM, fourth to n^(th)conditional probability vectors are determined by selecting one of thereceived values α and β according to the form of a combinationconstellation diagram, using the following mathematical expression (L)in the case of α*β≧0, and substituting the received value selected inthe mathematical expression (L) with the received value that is notselected in the expression in the case of α*β<0, where in themathematical expression (L), {circle around (a)} ifm*2^(n−k+3)−1<|Ω|≦m*2^(n−k+3)+1, the output is determined asa*(−1)^(m+1), also, {circle around (b)} if(2l−1)*2^(n−k+2)−1<|Ω|≦(2l−1)*2^(n−k+2)+1, the output is determined asa*(−1)^(l+1){0.9375(|Ω|−0.9375(2l−1)*2^(n−k+2)), also, {circle around(c)} if (P−1)*2^(n−k+2)+1<|Ω|≦P*2^(n−k+2)−1, when P is an odd number,the output is determined as${a*\left\lbrack {{\frac{0.0625}{2^{n - K + 2} - 2}\left\lbrack {{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 2}} + 1} \right\rbrack}} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}} \right\rbrack},$ when P is an even number, the output is determined as${a*\left\lbrack {{\frac{0.0625}{2^{n - k + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 2}} - 1} \right)}} \right\rbrack} + \left( {- 1} \right)^{{p/2} + 1}} \right\rbrack},$where k is conditional probability vector numbers (4, 5, . . . , n), Ωis a selected and received value, ‘a’ is an arbitrary real number setaccording to a desired output scope, α is a received value of I (realnumber) channel, β is a received value of Q (imaginary number) channel,m=0, 1, . . . 2^(k−3), l is 1, 2, . . . 3^(k−3), and p=1, 2 . . . ,2^(k−2).
 22. The method according to claim 21, wherein when themagnitude of QAM is more than 256-QAM, a method for obtaining an(n+2)^(th) conditional probability vector is the same as the method forobtaining the fourth conditional probability vector in the case that themagnitude of QAM of the second form is less than 256-QAM.
 23. The methodaccording to claim 21, wherein when the magnitude of QAM is more than256-QAM, (n+3)^(th) to (2n−1)^(th) conditional probability vectors arecalculated by substituting each of received values used with each of thereceived values that are not used when determining the fourth to n^(th)conditional probability vectors in the cases of α*β≧0 and α*β<0 when themagnitude of QAM of the second form is more than 256-QAM.
 24. The methodaccording to claim 21, wherein when the magnitude of QAM is more than256-QAM, a 2n^(th) conditional probability vector is calculated bysubstituting each of the received values used with each of the receivedvalues that are not used when determining the fourth to the (n+1)^(th)conditional probability vectors in the cases of α*β≧0 and α*β<0 when themagnitude of QAM of the second form is more than 256-QAM.
 25. The methodaccording to claim 1, wherein when the magnitude of QAM is more than256-QAM, (n+1)^(th) conditional probability vectors are determined usingthe following mathematical expression (M) in the case of α*β≧0, andsubstituting the received value selected in the mathematical expression(M) with the received value that is not selected in the expression inthe case of α*β<0, where in the mathematical expression (M), {circlearound (a)} if m*2²−1≦|Ω|≦m*2²+1, the output is determined asa*(−1)^(m+1), also, {circle around (b)} if (2l−1)*2¹−1<|Ω|≦(2l−1)*2¹+1,the output is determined as a*(−1)^(l+1){0.9375{(|Ω|−0.9375(2l−1)*2¹),where Ω is a selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value ofI (real number) channel, β is a received value of Q (imaginary number)channel, m=0, 1, . . . 2^(k−2), and l is 1, 2, . . . 3^(k−2).
 26. A softdecision method for demodulating a received signal α+βi of a squareQuadrature Amplitude Modulation (QAM) consisting of an in-phase signalcomponent and a quadrature phase signal component, comprising: receivingthe signal α+βi in a radio communication apparatus; obtaining aplurality of conditional probability vector values, each being a softdecision value corresponding to a bit position of a hard decision, usinga function including a conditional determination operation from thequadrature phase component and the in-phase component of the receivedsignal, wherein a first conditional probability vector decision methodfor demodulating a first half of a total number of bits is the same as asecond conditional probability vector decision method for demodulating asecond half of the bits, and is determined by substituting a quadraturephase component value and an in-phase component value with each other,wherein the demodulate signal has 2n bits, wherein the conditionalprobability vector values corresponding to the first bit to n^(th) bitof the first half are demodulated by one of the received signalcomponents α and β, and the conditional probability vector valuescorresponding to the (n+1)^(th) to 2n^(th) bits of the second half aredemodulated by the remaining one of the received signal components α andβ, and an equation applied for the two demodulations is the same in thefirst half and the second half, and wherein a first conditionalprobability vector is determined by selecting one of the received signalcomponents α and β according to a combination constellation diagram andapplying the following mathematical expression, where {circle around(1)} an output value is unconditionally determined as${\frac{a}{2^{n}}\Omega},$ where Ω is a selected and received valuewhich is one of α and β, and α is an arbitrary real number set accordingto a desired output scope.
 27. A soft decision method for demodulating areceived signal α+βi of a square Quadrature Amplitude Modulation (QAM)consisting of an in-phase signal component and a quadrature phase signalcomponent, comprising: receiving the signal α+βi in a radiocommunication apparatus; obtaining a plurality of conditionalprobability vector values, each being a soft decision valuecorresponding to a bit position of a hard decision, using a functionincluding a conditional determination operation from the quadraturephase component and the in-phase component of the received signal,wherein a conditional probability vector decision method fordemodulating a first half of a total number of bits is the same as adecision method for demodulating the remaining half of the bits, and isdetermined by substituting a quadrature phase component value and anin-phase component value with each other, wherein the demodulate signalhas 2n bits, wherein the conditional probability vector valuescorresponding to the first bit to n^(th) bit of the first half aredemodulated by one of the received signal components α and β, and theconditional probability vector values corresponding to the (n+1)^(th) to2n^(th) bits of the second half are demodulated by the remaining one ofthe signal components α and β, and an equation applied for the twodemodulations is the same in the first half and the second half, andwherein a second conditional probability vector is determined by thereceived value selected when determining a first conditional probabilityvector and by employing the following mathematical expression, where anoutput value is unconditionally determined as${a\left( {c - {\frac{c}{2^{n - 1}}{\Omega }}} \right)},$ where Ω is aselected and received value, n is a magnitude of the QAM, that is, aparameter used to determine 2^(2n), a is an arbitrary real number setaccording to a desired output scope, and c is an arbitrary constant. 28.A soft decision method for demodulating a received signal α+βi of asquare Quadrature Amplitude Modulation (QAM) consisting of an in-phasesignal component and a quadrature phase signal component, comprising:receiving the signal α+βi in a radio communication apparatus; obtaininga plurality of conditional probability vector values, each being a softdecision value corresponding to a bit position of a hard decision, usinga function including a conditional determination operation from thequadrature phase component and the in-phase component of the receivedsignal, wherein a conditional probability vector decision method fordemodulating a first half of a total number of bits is the same as adecision method for demodulating the remaining half of the bits, and isdetermined by substituting a quadrature phase component value and anin-phase component value with each other, wherein the demodulate signalhas 2n bits, wherein the conditional probability vector valuescorresponding to the first bit to n^(th) bit of the first half aredemodulated by one of the received signal components α and β, and theconditional probability vector values corresponding to the (n+1)^(th) to2n^(th) bits of the second half are demodulated by the remaining one ofthe signal components α and β, and an equation applied for the twodemodulations is the same in the first half and the second half, andwherein third to n^(th) conditional probability vectors are determinedby a received value set when determining a first conditional probabilityvector and employing the following mathematical expression (A), where inthe mathematical expression (A), first, dividing an output diagram in ashape of a basic V form, wherein conditional probability vectorcorresponding to each bit is divided into (2^(k−3)+1) areas, determininga basic expression according to$a\left( {{\frac{d}{2^{n - k + 1}}{\Omega }} - d} \right)$ determiningan output finding an involved area using a given Ω and substituting avalue of (|Ω|−m) such that a middle value is subtracted from each areainto the basic expression as a new Ω, and rendering the middle value asm=2^(n) and substituting the value of (|Ω|−m) into the basic expressionas a new Ω in an area that is in the most outer left and right sidesamong the divided areas, that is, (2^(k−2)−1)2^(n−k+2)<|Ω|, where Ω is aselected and received value, n is a magnitude of the QAM, that is, aparameter used to determine 2^(2n), k is conditional probability vectornumber (k=3, 4, . . . , n), d is a constant that changes according tothe value of k, and a is a constant determining an output scope.
 29. Themethod according to claim 28, wherein the (n+1)^(th) to 2n^(th)conditional probability vectors are sequentially obtained using one ofthe received values of α and β that is not selected when the firstconditional probability vector is determined and the mathematicalexpressions described above, except that the number k of the conditionalprobability vector included in the mathematical expression (A)sequentially substitutes 3 to n with n+1 to 2n).